Problem: Simplify the following expression: $\sqrt{150}-\sqrt{6}+\sqrt{54}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{150}-\sqrt{6}+\sqrt{54}$ $= \sqrt{25 \cdot 6}-\sqrt{6}+\sqrt{9 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{6}-\sqrt{6}+\sqrt{9} \cdot \sqrt{6}$ $= 5\sqrt{6}-\sqrt{6}+3\sqrt{6}$ Finally, simplify by combining the terms. $= ( 5 - 1 + 3 )\sqrt{6} = 7\sqrt{6}$